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Multiple Choice
For hydrogen, what is the wavelength of the photon emitted when an electron drops from the n=3 level to the n=2 level? The Rydberg constant is 1.097 × 10^7 m^-1.
A
486 nm
B
410 nm
C
434 nm
D
656 nm
Verified step by step guidance
1
Understand that the problem involves calculating the wavelength of a photon emitted during an electron transition in a hydrogen atom. This is done using the Rydberg formula for hydrogen.
The Rydberg formula is given by: , where is the wavelength, is the Rydberg constant, and are the principal quantum numbers of the initial and final energy levels.
Identify the values for the quantum numbers: is 2 and is 3. Substitute these values into the Rydberg formula.
Substitute the Rydberg constant value into the formula.
Solve for by calculating the difference in the reciprocals of the squares of the quantum numbers, then take the reciprocal of the result to find the wavelength in meters, and convert it to nanometers.